On asymptotical behavior of solution of Riccati equation arising in linear filtering with shifted noises

  • Agamirza E. Bashirov
  • Zeka Mazhar


In this paper we consider a linear signal system together with the two linear observation systems. The observation systems differ from each other by the noise processes. The noise of one of them is a constant shift in time of the signal noise. In the other one the shift is neglected. Respectively, we consider two best estimates of the signal corresponding to two different observation systems. The following problem is investigated: whether the effect of the shift on the best estimate becomes negligible as time increases. This leads to a comparison of the asymptotical behaviors of the solutions of respective Riccati equations. It is proved that under a certain relation between the parameters, the effect of the shift is not negligible.


Asymptotical Behavior Riccati Equation Time Moment Observation System Stochastic Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Ben92]
    Bensoussan, A.: Stochastic Control of Partially Observable Systems. Cambridge Univ Press, Cambridge (1992)MATHGoogle Scholar
  2. [CP78]
    Curtain, R.F., Pritchard, A.J.: Infinite Dimensional Linear Systems Theory, Lect. Notes Contr. and Inf. Sci. Vol.8. Springer, Berlin (1978)Google Scholar
  3. [LS98]
    Liptser, R.S., Shiryaev, A.N.: Statistics of Random Processes 2: Applications. Springer, New York (1998)Google Scholar
  4. [Dav77]
    Davis, M.H.A.: Linear Estimation and Stochastic Control. Chapman and Hall, London (1977)MATHGoogle Scholar
  5. [FR75]
    Fleming, W.H., Rishel R.W.: Deterministic and Stochastic Optimal Control. Springer, New York (1975)MATHGoogle Scholar
  6. [BJ68]
    Bucy, R.S., Joseph, P.D.: Filtering for Stochastic Processes with Application to Guidance. Interscience, New York (1968)Google Scholar
  7. [CJ04]
    Crassidis, J.L., Junkins, J.L.: Optimal Estimation of Dynamic Systems. Chapman and Hall, Boca Raton (2004)MATHGoogle Scholar
  8. [Bash03]
    Bashirov, A.E.: Partially Observable Linear Systems under Dependent Noises. Birkhäuser Verlag, Basel (2003)MATHGoogle Scholar
  9. [Bash05]
    Bashirov, A.E.: Filtering for linear systems with shifted noises. Inter. J. Contr., 78(7), 521–529 (2005)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Agamirza E. Bashirov
    • 1
    • 2
  • Zeka Mazhar
    • 1
  1. 1.Department of MathematicsEastern Mediterranean UniversityGazimagusa, Mersin 10Turkey
  2. 2.Institute of CyberneticsNational Academy of SciencesBakuAzerbaijan

Personalised recommendations